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T here has been a recent surge of interest in matrix and tensor factorization (decomposition), which provides meaningful latent (hidden) components or features with physical or physiological meaning and interpretation. Nonnegative matrix factorization (NMF) and its extension to three-dimensional (3-D) nonnegative tensor factorization (NTF) attempt to… (More)

- Andrzej Cichocki, Rafal Zdunek, Shun-ichi Amari
- ICA
- 2006

In this paper we discus a wide class of loss (cost) functions for non-negative matrix factorization (NMF) and derive several novel algorithms with improved efficiency and robustness to noise and outliers. We review several approaches which allow us to obtain generalized forms of multiplicative NMF algorithms and unify some existing algorithms. We give also… (More)

- Andrzej Cichocki, Rafal Zdunek, Shun-ichi Amari
- 2006 IEEE International Conference on Acoustics…
- 2006

In this paper we develop several algorithms for non-negative matrix factorization (NMF) in applications to blind (or semi blind) source separation (BSS), when sources are generally statistically dependent under conditions that additional constraints are imposed such as nonnegativity, sparsity, smoothness, lower complexity or better predictability. We… (More)

- Andrzej Cichocki, Rafal Zdunek, Shun-ichi Amari
- ICA
- 2007

In the paper we present new Alternating Least Squares (ALS) algorithms for Nonnegative Matrix Factorization (NMF) and their extensions to 3D Nonnegative Tensor Factorization (NTF) that are robust in the presence of noise and have many potential applications, including multi-way Blind Source Separation (BSS), multi-sensory or multi-dimensional data analysis,… (More)

- Rafal Zdunek, Andrzej Cichocki
- ICAISC
- 2006

Non-negative matrix factorization (NMF) is an emerging method with wide spectrum of potential applications in data analysis, feature extraction and blind source separation. Currently, most applications use relative simple multiplicative NMF learning algorithms which were proposed by Lee and Seung, and are based on minimization of the Kullback-Leibler… (More)

- Rafal Zdunek, Andrzej Cichocki
- IEEE Transactions on Signal Processing
- 2008

The focal underdetermined system solver (FOCUSS) algorithm has already found many applications in signal processing and data analysis, whereas the regularized M-FOCUSS algorithm has been recently proposed by Cotter for finding sparse solutions to an underdetermined system of linear equations with multiple measurement vectors. In this paper, we propose three… (More)

- Rafal Zdunek, Andrzej Cichocki
- Signal Processing
- 2007

Nonnegative Matrix Factorization (NMF) solves the following problem: find nonnegative matrices A ∈ RM×R + and X ∈ RR×T + such that Y ∼= AX, given only Y ∈ RM×T and the assigned index R. This method has found a wide spectrum of applications in signal and image processing, such as blind source separation, spectra recovering, pattern recognition, segmentation… (More)

- Constantin Popa, Rafal Zdunek
- Mathematics and Computers in Simulation
- 2004

The Algebraic Reconstruction Technique (ART), based on the well known algorithm proposed by S. Kaczmarz in 1937, is one of the most important class of solution methods for image reconstruction problems. But unfortunately, almost all the methods from the ART class give satisfactory results only in the case of consistent problems. In the inconsistent case… (More)

- Andrzej Cichocki, Rafal Zdunek
- Int. J. Neural Syst.
- 2007

The most popular algorithms for Nonnegative Matrix Factorization (NMF) belong to a class of multiplicative Lee-Seung algorithms which have usually relative low complexity but are characterized by slow-convergence and the risk of getting stuck to in local minima. In this paper, we present and compare the performance of additive algorithms based on three… (More)